Classically the study of PDEs on moving domains involved handling the equations on a given stationary domain.
The work [1]} introduced a moving space framework whereby the equations are posed in time-dependent Bochner spaces.
Shortly after, [2]} extended this to general Hilbert spaces, with examples given in [3]} and to Banach spaces in [4]}.
Non-linear extensions have been considered in [5]}, [6]} and non-local in [7]}.
These examples and extensions however do not cover incompressible fluid equations.
